I love watching horror movies, but nine out of ten times the heroes are woefully unprepared, and I sit there figuring out better ways to do things in order to survive.
1. As a nurse I can tell you that at for the first three days or so after death and reanimation, the zombies will be moving at near-regular speed, but after that as muscular decay and necrosis sets in they will get slower and clumsier. Within two weeks they would collapse in jellified heaps of rotting flesh and organs, so forget the "fast-movers" from Dawn of the Dead.
2. I wouldn't even try to get away, I have everything that I need at home. And really, where would I go? I live in West Virginia, in a small town away from large population centers. If I did have to clear out, I would be driving my Dodge Grand Caravan. It has enough room to take what I need and the size and weight to roll right over any undead in my way. A small, well-equipped, well-armed and armored group could do well moving cross-country, as long as they stayed sharp and worked together as a team. Most zombies wouldn't have the coordination to travel at any real speed over rough terrain and would fall far behind. They would doubtless gain back ground when the group had to make camp to rest, but if the camp was well-placed and guarded using sentinels and simple string alarms at 5 and 10 minutes distance the whole camp could be struck, on the move, or in place to initiate a counter-attack before the zombies arrived.
3. The first thing I would do at home would be to move my armor and weapons into the attic. (Never, ever take refuge in a basement or underground area - you are trapped, as there is only one way out, and if they get thru the door you are dead or worse.) I am in the SCA, and my armor (steel chainmail hauberk, thick aircraft aluminum plate armor, and large "heater" shield) is built to take full strength hits at speed from baseball bat-like rattan swords, so no zombie even has a hope of scratching it with teeth and fingernails. My weapons include several swords, all of which are full-tang construction and made of strong steel, and all of which I can use well. Guns are OK in a pinch, but require ammo and can jam at the worst times. Baseball bats, crowbars, and other bludgeoning weapons can do okay, but they are usually not balanced for combat and tend to be tip heavy, which throws you off-balance when you swing and makes the weapon difficult and unwieldy. An axe has incredible shearing power, but only has a small area of effective blade and again is incredibly tip-heavy. Machetes are thin, usually stamped out of rolled steel, and have little to no heat tempering. Lacking a "spine" - the thicker middle of a blade's cross-section, a machete tends to bend when it is used against thick bone structures. Fighting for almost twenty years in the SCA has taught me that the sword, well-balanced, (esp. the Japanese katana) has the quickest recovery time and allows the warrior to strike and defend multiple times while an axeman is delivering one or two attacks.
Once I am in the attic I would pull the stairs up after me and armor up. If any zombies were in the house I would drop the stairs and let them come up one at a time, because it is ridiculously easy to decapitate someone coming headfirst up a set of stairs. Fight in doorways as well in order to limit the number of attackers that can reach you at any given minute.
4. Never go for the headshot with a melee weapon - it can become lodged in the skull. Always swing for the neck to sever the spinal column as it is the only bony structure there, or take off hands and legs. A legless zombie can't chase you too well, and a handless one can't grab you. The only "vital" organ a zombie has is its brain, so you must either damage it to the point where it can no longer function i.e. send electrical impulses to the musculature, or separate it from the body completely i.e. decapitation. Attempting to thrust your weapon into a zombies body will do no real damage at all - instead concentrate on severing lower arm/hand areas, ankles, and of course, the neck. Remember that a zombie can only ever be as fast, strong, and tough as he was while alive, and will within days become slower and weaker. Despite all movie assertions that a zombie can scratch, claw, and bite his way thru just about anything, this simply is not true. As my swordbrother Leecifer pointed out, "Ever try to bite thru a good leather coat? Try it sometime." Armor made from thicker saddle leather would be even more durable, not to mention the supreme protective power of chainmail or plate. (And no one can tell me that the mall in the Dawn of the Dead remake, being that close to a large body of water, didn't have a scuba shop where they could have found chainmail fish fillet gloves and shirts/suits of sharkmail - which is nothing more than titanium/stainless steel alloy chainmail, of such fine weave that it would make an Elven armorer proud, and able to resist the sawing teeth of a shark.)
Once the house was emptied of threats I would set about barricading doors and windows and inventorying how much canned food I had, filling up as many jerry cans and milk jugs as possible with water, and taking stock of my first aid supplies. You cannot assume that electric, gas, and water services will stay on long, so I would eat any perishable foodstuffs first and recharge any electric devices such as a power drill and a sportlight (mine is five million candlepower and the lantern function can run for eight total hours on a full charge).
5. Any restaurants in the area would also suffer a loss of power and therefore their food would also spoil. Food in their freezers might last a few more days, but at one time I was a restaurant manager and I can tell you that nine out of ten times the freezer is locked. A better choice for raids is the supermarket canned goods aisle, as well as their pharmacy for antibiotics (I'm a nurse, I know what I'm looking for), but remember that you may also be in competition or conflict with other survivors for such resources, and they will be wanting to take what you have as well - you may be forced to defend yourself against other humans. Good food choices are all canned goods, Ramen noodles, presweetened Kool-aid packets, canned juices, hard candies, pudding cups, pop tarts, bottled water, and various other non-perishable, non-refrigerated foodstuffs. Stay away from bread and milk, as they spoil far too quickly. Concentrate instead on things that can be heated on a campstove or over a campfire, and reconstituted with water, like Ramen noodles. If you are using non-bottled water for cooking, boil it for at least five minutes to kill any bacteria.
6. Soon I would be reconnoitering the area to see how many people had survived uninfected, and eliminating any zombies around by drawing them out and engaging them in single combat or in twos and threes so as not to get surrounded. Always keep on the move and change your direction of travel often to prevent them cutting across your intended path or surrounding you. I don't live near a graveyard, so the only undead around would have to be the newly dead. Any corpse (human or animal) that has been dead for over three weeks or so probably would not reanimate simply because of the level of decay present. Because of this I might wait a few days before scouting in order to give any viable undead time to further decay. As their bodies start to decompose they would get slower and weaker, becoming easier to dispatch or dodge. Within two to three weeks the whole zombie plague would fall apart as they decay past any point of muscular viability. A fresh, newly dead zombie will be just as fast and strong as he was in life, but give it a few days and they decay.
7. "Blending in" with them is usually not an option, as they can smell your blood and sense your heart beating from a temporary enhancement of the sensory organs by the Z-factor. Anyone trying to do so is committing suicide.
8. As for other "Hollywood" refuges, a'la Dawn of the Dead, I would never, ever, head for a mall or other large public area - far too undefendable (and why in the world they didn't build or find armor of some type - like the aforementioned sharkmail - while they were in the mall all that time I'll never know). I would also not place my trust in river islands as a refuge unless the current was deep and fast: zombies cannot drown, so theoretically they can float to the island like so much deadwood (and as decay sets in they would be bloating with gases so they would most likely float) or walk across the bottom (as the pirate crew did in PotC:CotBP) to you if the water is slow. Ocean islands are better, but you must be sure they are uninhabited first, and never dock your boat initially - anchor it out a ways and row in with a canoe, that way if there are too many to fight at first you can pick off a few and then retreat to your boat, rinse and repeat until the beach is clear. For me it is a moot point - I am nowhere near the coast - but I do live 150 yards from a large, deep, fast-moving river. The Kanawha empties into the Ohio, the Ohio empties into the Mississippi, and the Mississippi empties into the Gulf of Mexico, but that is a journey of thousands of miles. A much better idea (at least in WV) is to flee to the tops of some of these strip-mined mountaintops where they have mined around the bedrock cone, leaving an artificial mesa, still forested on top and absolutely inaccessible to anyone without a rope and grappling hook. (Got one of those, too.) Set up camp on top and wait 'em out. Chances are that they will never track you down anyway, and if they do and you have a gun, it's target practice time as the whole area surrounding the mesa is open field conditions with no cover.
9. If I was able to stay in one place I would make sure that it was easy to see that I was a survivor in order to avoid the fate of Ben in Night of the Living Dead - living thru the ordeal just to get mistaken for a zombie and headshot. I would exit the attic and set up "camp" on the roof, with radio, dome tent, and a big sign. So what if I attract a few zombies? Without any way of getting to me they would simply mill about on the ground until I snuck down the back of the house using our rope fire escape ladder (which I would keep on the roof) and decapitated a few at a time as they slowly came around the house. I do not believe that after three days any would have the ability or coordination to climb, but I would make it a priority to take out newly dead fast-movers first. Traps could be set using abandoned houses - get a whole pack chasing you, run inside a previously scouted and prepared house, let them enter and then run out the back door, slam it and drop a crossmember 2x4 as a brace across the door. Run back to the front and brace that door too. Light match. Ignite the house that you previously doused with gasoline. Eliminate a whole pack in one fell swoop. Rinse and repeat.
10. Various gear I have at hand right now that I would find useful:
Binoculars, Rope and Grappling hook, Coleman lantern, 5-cell Maglite, matches or lighters, can opener, battery operated perimeter alarms, canteen, mess kit, liquid fuel operated campstove, sleeping bag, backpack, handcuffs, armor repair kit, handaxe, whetstone and metal file, toiletries, flare gun, inflatable raft, and a canoe.